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(10) Let f RR be the function given by f(x) = e and g (1,7) →R be given by g(x) = tan x. (a) Is fog injective? If no, can we restrict either the domain of f or g so that fog is surjective? (b) Is fog surjective? If no, can we restrict either the image (range) of f or g so that fog is surjective? (c) Is fog bijective? If no, can we restrict either the domain of f or g, or the image (range) of or g, so that fog is bijective?

(10) Let f RR be the function given by f(x) = e and g (1,7) →R be given by g(x) = tan x. (a) Is fog injective? If no, can we restrict either the domain of f or g so that fog is surjective? (b) Is fog surjective? If no, can we restrict either the image (range) of f or g so that fog is surjective? (c) Is fog bijective? If no, can we restrict either the domain of f or g, or the image (range) of or g, so that fog is bijective?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(10) Let f RR be the function given by f(x) g(x) = tan x. = e* and g : (-) → R be given by (a) Is fo g injective? If no, can we restrict either the domain of f or g so that fog is surjective? (b) Is fog surjective? If no, can we restrict either the image (range) of f or g so that fog is surjective? (c) Is fog bijective? If no, can we restrict either the domain of f or g, or the image (range) of f or g, so that fog is bijective?
Transcribed Image Text:(10) Let f RR be the function given by f(x) g(x) = tan x. = e* and g : (-) → R be given by (a) Is fo g injective? If no, can we restrict either the domain of f or g so that fog is surjective? (b) Is fog surjective? If no, can we restrict either the image (range) of f or g so that fog is surjective? (c) Is fog bijective? If no, can we restrict either the domain of f or g, or the image (range) of f or g, so that fog is bijective?
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